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Topic: fom - 01 - preface
Replies: 35   Last Post: Dec 16, 2012 12:20 AM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 9, 2012 4:06 AM

On 9 Dez., 03:06, fom <fomJ...@nyms.net> wrote:

> > A question: Do you believe that there are more than countably many
> > finite words?
> > Do you believe that you can use infinite words (not finite
> > descriptions of infinite sequences).
> > Do you believe that you can put in order what you cannot distinguish?

>
> There is a certain history here.
>
> As set theory developed, Cantor was confronted
> with the notion of "absolute infinity".

He found it in the holy bible and with St. Augustin.
>
> I prefer to go with Kant:
>
> "Infinity is plurality without unity"
>
> and interpret the objects spoken of in typical
> discussions of set theory as transfinite numbers.

Unfortunately that does not answer my question because these
transfinite numbers belong to a countable set.

> But, I side with
> Aristotle on the nature of what roles are played
> by a deductive calculus.

Aristotle rejected actual infinity in mathematics. He said: Our
account does not rob the mathematicians of their science, by
disproving the actual existence of the infinite in the direction of
increase, in the sense of the untraversable. In point of fact they do
not need the infinite and do not use it.

> Scientific demonstration
> is distinct from dialectical argumentation that
> argues from belief. In turn, that distinction
> informs that a scientific language is built up
> synthetically. The objects of that language
> are individually described using definitions.
> The objects of that language are individually
> presumed to exist.

Yes, that's matheology: belief without proof.

Consequently, the
> names which complete the "incomplete symbols"
> exist as references only by virtue of the fact
> that the first names introduced for use in the
> science are a well-ordered sequence.

>
> Since I cannot possibly defend introducing
> more than some finite number of names in
> this fashion, the assumption of transfinite
> numbers in set theory has a consequence. It
> can be reconciled with this position only
> if models of set theory are admissible as
> such when they have a global well-ordering.

Like the 10^140 monkeys in Indian mythology. As scientific and as
useful.

Regards, WM

Date Subject Author
12/7/12 fom
12/8/12 Zaljohar@gmail.com
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 fom
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/8/12 fom
12/8/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/10/12 mueckenh@rz.fh-augsburg.de
12/10/12 Virgil
12/10/12 fom
12/10/12 ross.finlayson@gmail.com
12/11/12 fom
12/12/12 ross.finlayson@gmail.com
12/12/12 Virgil
12/16/12
12/9/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 ross.finlayson@gmail.com
12/9/12
12/10/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/9/12 Zaljohar@gmail.com
12/9/12 mueckenh@rz.fh-augsburg.de
12/10/12 Dan Christensen
12/11/12 fom